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Geometry is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the third century B.C., geometry was put into an axiomatic form by Euclid, whose treatment - Euclidean geometry - set a standard for many centuries to follow. The field of astronomy, especially mapping the positions of the stars and planets on the celestial sphere, served as an important source of geometric problems during the next one and a half millennia.

This EMS volume consists of two parts. The first part is devoted to the exposition of the cohomology theory of algebraic varieties. The second part deals with algebraic surfaces. The authors have take…